Membrane locking and reduced integration for curved elements

H. Stolarski, T. Belytschko

Research output: Contribution to journalArticlepeer-review

190 Scopus citations


The behavior of a curved beam element is studied by comparison to an analytic solution. In the curved beam element, curvature effects are incorporated through a “shallow-shell” type theory. It is shown that when low-order, inplane displacement fields are used for the element, the curvature terms increase the bending stiffness due to contributions from the membrane strains; this is called “membrane locking." Reduced integration yields a bending stiffness, which is in better agreement with the analytic value, and yet it retains the bending-membrane coupling, which is characteristic of curved elements. The results of the analysis are verified by several numerical examples.

Original languageEnglish (US)
Pages (from-to)172-176
Number of pages5
JournalJournal of Applied Mechanics, Transactions ASME
Issue number1
StatePublished - Mar 1982


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